Template protection techniques are privacy and security enhancing techniques of biometric reference data within a biometric system. Several of the template protection schemes known in the literature require the extraction of a binary representation from the real-valued biometric sample, which raises the question whether the bit extraction method reduces the classification performance. In this work we provide the theoretical performance of the optimal log likelihood ratio continuous classifier and compare it with the theoretical performance of a binary Hamming distance classifier with a single bit extraction scheme as known from the literature. We assume biometric data modeled by a Gaussian between-class and within-class probability density with independent feature components and we also include the effect of averaging multiple enrolment and verification samples.